249 research outputs found
New solution of the Supersymmetric KdV equation via Hirota methods
We consider the resolution of the supersymmetric KdV equation
with () from the Hirota formalism. For the first time, a
bilinear form of the equation is constructed. We construct
multisoliton solutions and rational similarity solutions.Comment: 7 pages, 9 figures. arXiv admin note: significant text overlap with
arXiv:1104.059
Rational solutions of the discrete time Toda lattice and the alternate discrete Painleve II equation
The Yablonskii-Vorob'ev polynomials , which are defined by a second
order bilinear differential-difference equation, provide rational solutions of
the Toda lattice. They are also polynomial tau-functions for the rational
solutions of the second Painlev\'{e} equation (). Here we define
two-variable polynomials on a lattice with spacing , by
considering rational solutions of the discrete time Toda lattice as introduced
by Suris. These polynomials are shown to have many properties that are
analogous to those of the Yablonskii-Vorob'ev polynomials, to which they reduce
when . They also provide rational solutions for a particular
discretisation of , namely the so called {\it alternate discrete}
, and this connection leads to an expression in terms of the Umemura
polynomials for the third Painlev\'{e} equation (). It is shown that
B\"{a}cklund transformation for the alternate discrete Painlev\'{e} equation is
a symplectic map, and the shift in time is also symplectic. Finally we present
a Lax pair for the alternate discrete , which recovers Jimbo and Miwa's
Lax pair for in the continuum limit .Comment: 23 pages, IOP style. Title changed, and connection with Umemura
polynomials adde
Axonal Odorant Receptors Mediate Axon Targeting
In mammals, odorant receptors not only detect odors but also define the target in the olfactory bulb, where sensory neurons project to give rise to the sensory map. The odorant receptor is expressed at the cilia, where it binds odorants, and at the axon terminal. The mechanism of activation and function of the odorant receptor at the axon terminal is, however, still unknown. Here, we identify phosphatidylethanolamine- binding protein 1 as a putative ligand that activates the odorant receptor at the axon terminal and affects the turning behavior of sensory axons.Genetic ablation of phosphatidylethanolamine-binding protein 1 in mice results in a strongly disturbed olfactory sensory map. Our data suggest that the odorant receptor at the axon terminal of olfactory neurons acts as an axon guidance cue that responds to molecules originating in the olfactory bulb. The dual function of the odorant receptor links specificity of odor perception and axon targeting
An efficient algorithm to calculate intrinsic thermoelectric parameters based on Landauer approach
The Landauer approach provides a conceptually simple way to calculate the
intrinsic thermoelectric (TE) parameters of materials from the ballistic to the
diffusive transport regime. This method relies on the calculation of the number
of propagating modes and the scattering rate for each mode. The modes are
calculated from the energy dispersion (E(k)) of the materials which require
heavy computation and often supply energy relation on sparse momentum (k)
grids. Here an efficient method to calculate the distribution of modes (DOM)
from a given E(k) relationship is presented. The main features of this
algorithm are, (i) its ability to work on sparse dispersion data, and (ii)
creation of an energy grid for the DOM that is almost independent of the
dispersion data therefore allowing for efficient and fast calculation of TE
parameters. The inclusion of scattering effects is also straight forward. The
effect of k-grid sparsity on the compute time for DOM and on the sensitivity of
the calculated TE results are provided. The algorithm calculates the TE
parameters within 5% accuracy when the K-grid sparsity is increased up to 60%
for all the dimensions (3D, 2D and 1D). The time taken for the DOM calculation
is strongly influenced by the transverse K density (K perpendicular to
transport direction) but is almost independent of the transport K density
(along the transport direction). The DOM and TE results from the algorithm are
bench-marked with, (i) analytical calculations for parabolic bands, and (ii)
realistic electronic and phonon results for .Comment: 16 Figures, 3 Tables, submitted to Journal of Computational
electronic
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